To factor the given expression [tex]\( v^2 - 4 \)[/tex], we can use the difference of squares formula. The difference of squares formula is:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In the given expression [tex]\( v^2 - 4 \)[/tex], we can identify the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
- Here, [tex]\( a = v \)[/tex] because [tex]\( v^2 \)[/tex] matches the form [tex]\( a^2 \)[/tex].
- [tex]\( b = 2 \)[/tex] because [tex]\( 4 \)[/tex] can be written as [tex]\( 2^2 \)[/tex], which matches the form [tex]\( b^2 \)[/tex].
Now apply the difference of squares formula:
[tex]\[ v^2 - 4 = (v - 2)(v + 2) \][/tex]
So, the expression [tex]\( v^2 - 4 \)[/tex] factors to:
[tex]\[ \boxed{(v - 2)(v + 2)} \][/tex]
